WASHINGTON—The Obama administration is declassifying documents about its telephone spying program to try to tamp down congressional opposition to domestic surveillance.

The documents will provide little solace, however, to Americans hoping to understand the legal analysis that underpinned the widespread surveillance.

And the redacted documents show only in broad strokes how National Security Agency officials use the data.

One particular type of analysis, called "hop analysis" is hinted at but never fully discussed. That allows to the government to search the phone records of not only suspected terrorists, but everyone who called them, everyone who called those people, and others who called them, as well.

With that authority, the government can search the records of millions of people in an investigation of one person.

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